MATH 3339 Statistics for the Sciences Final Exam. SOLUTIONS

Question 1 Given a dataset of all positive values, if the largest value of a dataset is doubled, which of the following is not true? a) The variance increases b) The range increases c) The standard deviation incre ...

Question 1 Given a dataset of all positive values, if the largest value of a dataset is doubled, which of the following is not true? a) The variance increases b) The range increases c) The standard deviation increases d) The mean increases e) The interquartile range increases Question 2 Given that , find . a) 0.761 b) 0.124 c) 0.876 d) 0.239 e) 0.407 Question 3 A service center receives an average of 0.6 customer complaints per hour. Management's goal is to receive fewer than three complaints each hour. Assume the number of complaints follows the Poisson distribution. Determine the probability that exactly four complaints will be received during the next eight hours. a) 0.524 ( ) = 0.27, ( ) = 0.46, and ( ∩ ) = 0.11 ( ) Q3- Q IAB=PAB i = 0 .239 0 .6x8 = 4 . 8 ADF.tt meblethey'rean increasing MMAfffg gm.it on MAMMA b) 0.182 c) 0.476 d) 0.003 e) 1.000 Question 4 The following table displays the results of a sample of 100 in which the subjects indicated their favorite ice cream of three listed. The data are organized by favorite ice cream and age group. What is the probability that a person chosen at random will be under 20 years old if he or she favors chocolate? Age Chocolate Vanilla Strawberry Over 40 12 8 10 20-40 13 9 13 Under 20 13 19 3 a) b) c) d) e) Question 5 Suppose that in a large metropolitan area, 89% of all households have cable tv. Suppose you are interested in selecting a group of six households from this area. Let X be the number of households in a group of six households from this area that have cable tv. For what proportion of groups will at most two of the households have cable tv? a) 0.979 b) 0.998 87 100 25 38 13 38 13 30 13 100 MAY FEENETTE so Magaman Ie to rememberthis as EBAY.EEEEE.i 0 0018 0.002 c) 0.019 d) 0.021 e) 0.002 Question 6 A random sample of 144 observations produced a sample proportion of 0.35. An approximate 90% confidence interval for the population proportion p is between a) 0.285 and 0.415 b) 0.285 and 0.428 c) 0.310 and 0.390 d) 0.272 and 0.428 e) 0.269 and 0.431 Question 7 A potato chip company calculated that there is a mean of 73.6 broken potato chips in each production run with a standard deviation of 5.1. If the distribution is approximately normal, find the probability that there will be fewer than 71 broken chips in a run. a) 0.153 b) 0.695 c) 0.305 d) 0.605 e) 0.555 Question 8 Identify the most appropriate test to use for the following situation: A national computer retailer believes that the average sales are greater for salespersons with a college degree. A random sample of 14 salespersons with a degree had an average weekly sale of $3542 last year, while 17 salespersons without a college degree averaged $3301 in weekly sales. The standard deviations were $468 and $642 respectively. Is there evidence to support the retailer's belief? NY fm d f MSN.EE ETBiEEim a) Two sample z test for means b) Two sample z test for proportions c) Two sample t test for means d) One sample z test for proportions e) One sample t test for means f) Matched pairs t test for means g) One sample z test for means Question 9 The weights of male and female students in a class are summarized in the following boxplots: Which of the following is NOT correct? a) The mean weight of the female students is about 120 because of symmetry. b) The male students have less variability than the female students. c) About 50% of the male students have weights between 150 and 185 lbs. d) The median weight of the male students is about 166 lbs. Question 10 Data for gas mileage (in mpg) for different vehicles was entered into a software package and part of the ANOVA table is shown below: Source DF SS MS Vehicle 6 420 70.00 Error 7 303 43.29 Total 13 723 t test sample 7 test population e Man Determine the p-value for the data. a) 0.0162 b) 0.1356 c) 0.4652 d) 0.2712 e) 0.0904 Question 11 A random sample of 144 cans of fruit nectar is drawn from among all cans produced in a run. Prior experience has shown that the distribution of the contents has a mean of 12.25 ounces and a standard deviation of 2.14 ounce. What is the probability that the average contents of the 144 sample cans is less than 12.01 ounces? a) 0.223 b) 0.178 c) 0.822 d) 0.911 e) 0.089 Question 12 If the P-value is larger than the level of significance α, then the researcher should __________ at level α. a) Fail to reject H0 b) Reject H0 c) Accept H0 Question 13 For a specific location in a particularly rainy city, the time a new thunderstorm begins to produce rain (first drop time) is uniformly distributed throughout the day and independent of this first drop time for the surrounding days. Given that it will rain at some point both of the next two days, what is the probability that the first drop of rain will be felt between AM and PM on both days? 8 : 45 2 : 25 0 1st teststatistic V 62 That MSN.AMEMM¬phovm 12.01 12.25 2.14V44 0.089 lesswereject 1 45 a) 0.0557 b) 0.2361 c) 0.9416 d) 0.2417 e) 0.0584 f) None of the above. Question 14 The one-sample t statistic for a test of H0: μ = 15 vs. Ha: μ < 15 based on n = 15 observations has the test statistic value of t = -1.36. What is the p-value for this test? a) 0.902 b) 0.098 c) 0.398 d) 0.000 e) 0.195 Question 15 A student is taking their Statistics final exam. For a particlar problem there are three versions. All versions ask for a value of so that , where varies depending on the problem version. Assume that follows the following distrubution: Find . a) b) c) d) ( ≤ ) = ( = 0.67) = , 1 ( = 0.61) = , ( = 0.67) = 8 14 58 [ ] 0.821 0.552 0.768 0.827 8:45 - 2: 25 &t pop no z (ai + 5 . 667) Pt( - 1.36 , 14) quorm (0 . 67) ·t + qnorm (0 -61)I +anorm 10 .67)·E Margin 5.67 124 0.0558 MMMM iii In on MANNAREAE 10.399 e) f) Cannot be determined. Question 16 This is a written question, worth 11 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full credit. Problem Code: 1611 A person's muscle mass is expected to decrease with age. To explore this relationship in women, a nutritionist randomly selected 60 women aging from age 40 to 79 and measured their muscle mass. Using age as the explanatory variable and the muscle mass as the dependent variable, computer output of the data is as follows (the p-values are intentionally left blank): Predictor Coef StDev T P Constant 113.052 9.170 12.329 --- Age - 0.428 0.137 - 3.124 --- Part a: What is the regression equation? Part b: Calculate the 99% confidence interval of the slope of the regression line. Part c: Use the information provided to test whether there is a significant relationship between a person's age and muscle mass at the 5% level. a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted from my test for not working this problem. Question 17 This is a written question, worth 11 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full credit. Problem Code: 1744 The random variable has probability density function: Part a: Determine the value of . 0.400 ( ) = 16 - 18 0 0 ≤ ≤ 4 otherwise y Ear I ge ant y 113.052 0.4284 dt6020 0.428 CC1 qt1.991258 0.137 3.124 nu Pt 3.124,58 Part b: Find , the cumulative distribution function of . Part c: Find . Part d: Find the variance and standard deviation of . Part e: Determine the third quartile of . a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted from my test for not working this problem. Question 18 This is a written question, worth 11 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full credit. Problem Code: 1891 Employers would like to know which days of week employees are absent in a six-day work week. Previously employers believed that employees were absent equally during the week. Suppose a random sample of 60 managers were asked on which day of the week they had the highest number of employee absences. The results were distributed as in the table below. For the population of employees, do the days of highest number of absences occur with EQUAL frequencies during a six-day work week? Test at 5% significance level. Monday Tuesday Wednesday Thursday Friday Saturday 12 10 5 8 13 12 Part a: What type of test should be used in this situation? Part b: State the hypothesis. Part c: What is the test statistic? Part d: Find the p-value and state your conclusion. a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted from my test for not working this problem. Question 19 This is a written question, worth 11 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full credit. Problem Code: 1984 ( ) [ ] 2 goodness offit Ho absencesareequal Haabsencesareunequal 4 6 gfffffn.BEfaichisq.test 412.10158.13.12 F 4 The following data are for intelligence-test (IT) scores, reading rates (RR), and grade-point averages (GPA) of 8 at-risk students. IT 155 206 156 172 209 191 163 207 RR 43 33 27 35 25 36 36 26 GPA 3.0 2.0 1.7 2.5 2.0 2.7 2.6 1.8 Part a: Calculate the line of best fit that predicts the GPA on the basis of RR scores. Part b: Calculate the line of best fit that predicts the GPA on the basis of IT scores. Part c: Which of the two lines calculated in parts a and b best fits the data? Justify your answer. a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted from my test for not working this problem. Question 20 This is a written question, worth 11 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full credit. Problem Code: 2023 If the joint probability distribution of and is given by: Determine: Part a: Part b: Part c: Part d: a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted from my test for not working this problem. ( , ) = , for all + 2 = 0, 1, 2, 3 and = 0, 1, 2 42 ( ≤ 2, = 1) ( + = 4) ( + ) ( ) IT CC RR CC GPA L 1M GPA RR 1M GPA IT COV GPARR Cor OPA IT biggeravg.fi fymeans Ii.li a p x O 4 1 PL 4 1 PL 2 c E Y 442 3 42 4 42 420 9 lt942ttttyyztstislyz.tl HMtI b p 4 4 P x 2 4 2 P X 3,4 7 6 42 5142 420 11 131m